My wife and I recently purchased a house and are slowly going through and making repairs now that we've moved in. One thing that I noticed early on was that the towel racks in the ensuite bathroom were quite loose and wobbly, so I wanted to change them.
First attempt was to get some WallMate wall anchors to embed in the plasterboard, but no matter how hard I tried I couldn't get them into the plaster. Best I could manage was maybe 1-2mm deep before the anchor itself would start to deform.
Am I taking the wrong approach here, and if so what would you recommend? Any idea what the reason is I can't install the wall plugs? A drill goes through fine and there's no stud on the other end from what I can see. Thank you!
Here's a photo of where I tried to install the wall anchor. It is about 5cm from the shower tiles.

Unfortunately I've never had anyone to learn this stuff from, so hoping I can grow my knowledge with your help! Cheers!